The present invention relates generally to a zoom lens system, such as an image-taking apparatus, a projection apparatus, an exposure apparatus, and a reader apparatus. The present invention is particularly suitable for a small image-taking apparatus.
Along with the recent widespread of digital cameras and camera phones, an application field of small camera is increasingly spreading. For smaller sizes of such cameras, a smaller image-pickup device is increasingly demanded. In addition, the added values are also increasingly demanded, such as zooming, wide-angle arrangement, and high-definition performances. However, it is difficult to combine the miniaturization with the highly added values in view of the zooming scheme, because zooming usually needs movements of a lens along an optical path relative to a light-receiving surface, such as a CCD, and movements in the object direction extends an overall length of the optical system, preventing the miniaturization.
Prior art include U.S. Pat. Nos. 3,305,294 and 3,583,790, and Japanese Patent Application, Publication No. 01-35964. U.S. Pat. No. 3,305,294 provides each of a pair of lenses with a curved surface expressed by a cubic function, and shifts these two lenses in a direction different from the optical-axis direction for power variations and miniaturization. This lens is referred to as a so-called Alvarez lens. The Alvarez lens does not move in the optical-axis direction, and contributes to a reduction of the overall length. U.S. Pat. No. 3,583,790 proposes a removal of an aberration by providing a curved surface with high-order term, in particular, a quitic term. Japanese Patent Application, Publication No. 01-35964 propose that at least two lenses be arranged to change the power while the image point is maintained.
When a rotationally asymmetrical lens is included, no common axis is provided unlike a normal coaxial lens. Such a non-coaxial optical system is referred to as an off-axial optical system. Where a reference axis is defined as an optical path of the light that passes the center of an image and the center of the pupil, this optical system is defined as an optical system that includes an off-axial curved surface in which a surface normal at an intersection between the reference axis and a forming surface is not located on the reference axis. The reference axis has a bent shape, and thus a calculation of the paraxial amount should use the paraxial theory that relies upon the off-axial theory instead of the paraxial theory for a coaxial system. Optics Vol. 29, No. 3 (2000) implements this method by calculating a 4×4 matrix based on the curvature of the surface.
In designing a zoom lens system, U.S. Pat. Nos. 3,305,294 and 3,583,790 simply mention a method of using of a pair of rotationally asymmetrical lenses to change the power and to correct the aberration, and cannot maintain the image plane constant problematically. On the other hand, Japanese Patent Application, Publication No. 01-35964 discloses a principle to change the power while maintaining the image point constant, but does not actually design a zoom lens system through aberration corrections. An attempt was made to actually design a zoom lens system in accordance with Japanese Patent Application, Publication No. 01-35964. Prior to a discussion of the designed example, a description will be given of the way of expression of a specification in the embodiments and common matters to each embodiment.
The off-axial optical system has a bent reference axis as shown in FIG. 2. In an absolute coordinate system with an origin that is set at a center of a first surface, a reference axis is defined as a path which a ray that passes the origin and the pupil center traces. A Z-axis is defined as a line that connects the center of the image center to the origin of the absolute coordinate system as the center of the first surface, where a direction from the first surface to the center of the image is set positive. The Z-axis is referred to as an optical axis. A Y-axis is defined as a line that passes the origin and forms 90° with respect to the Z-axis in accordance with a rule of a right-hand coordinate system, and an X-axis is defined as a line that passes the origin and is orthogonal to the Y-axis and Z-axis. In this application, a paraxial value is a result of the off-axial paraxial tracing. Unless otherwise specified, it is a result of the off-axial paraxial tracing and a calculation of the paraxial value. In addition, an optical system has two or more rotationally asymmetrical, aspherical surfaces each having the following shape:z=C02y2+C20x2+C03y3+C21x2y+C04y4+C22x2y2+C40x4+C05y5+C23x2y3+C41x4y+C06y6+C24x2y4+C42x4y2+C60x6  [EQUATION 1]
Equation 1 includes only even-order terms with respect to “x,” and the curved surface defined by Equation 1 is symmetrical with respect to the yz plane.
When the following condition is met, Equation 1 is symmetrical with respect to the xz plane:C03=C21=C05=C23=C41=t=0  [EQUATION 2]
When the following conditions are met, Equation 1 is a rotationally symmetrical shape:C02=C20  [EQUATION 3]C04=C40=C22/2  [EQUATION 4]C06=C60=C24/3=C42/3  [EQUATION 5]
When the above conditions are not met, Equation 1 provides a rotationally asymmetrical shape.
A description will now be given of one actual design example of a zoom lens system in accordance with Japanese Patent Application, Publication No. 01-35964. The zoom lens system includes two pairs of rotationally asymmetrical lens units, which are labeled first and second units in order from an object side. First, these units are approximated by one thin lens for paraxial calculation purposes. The following equation is met, where φ1 and φ2 are the powers of these thin lenses of the first and second units, “e” is a principal point separation, “Sk” is a back-focus, φ is the power of the entire system, and “f” is a focal length:
                    ϕ        =                              1            f                    =                                    ϕ              1                        +                          ϕ              2                        -                          e              ⁢                                                          ⁢                              ϕ                1                            ⁢                              ϕ                2                                                                        [                  EQUATION          ⁢                                          ⁢          6                ]            
The back-focus Sk satisfies the following equation from the paraxial calculation:
                              S          k                =                              1            -                          e              ⁢                                                          ⁢                              ϕ                1                                              ϕ                                    [                  EQUATION          ⁢                                          ⁢          7                ]            
When the principal point separation e and back-focus Sk are determined, φ1 and φ2 are expressed as a function of the power φ of the entire system from Equations 6 and 7 or paths of power changes of the first and second units in the changes of the power of the entire system. When the principal point separation e=3 and the back-focus Sk=15, φ1 and φ2 become as follows:
                              ϕ          1                =                                            -              5                        ⁢            φ                    +                      1            3                                              [                  EQUATION          ⁢                                          ⁢          8                ]                                          ϕ          2                =                              1                          45              ⁢              φ                                -                      2            5                                              [                  EQUATION          ⁢                                          ⁢          9                ]            
FIG. 3 is a graph indicative of a relationship between φ1 and φ2 and the power φ of the entire system. As the power of the entire system increases, the first unit changes from positive to negative whereas the second conversely changes from negative to positive. Here, the rotationally asymmetrical curved surface is expressed by Equation 10, and a relationship between a coefficient “a” and the power is expressed by Equation 11:z=ay3+3ax2y  [EQUATION 10]φ=12aδ(n−1)  [EQUATION 11]
x, y and z denote above axes. δ is an offset amount in the Y-axis direction from the Z-axis of the two rotationally asymmetrical lenses, and n is a refractive index of the lens. Table 1 indicates coefficient “a” and “n” of the rotationally asymmetrical lens, and the offset amounts δ from the Z-axis at a telephoto end, a midpoint, and a wide-angle end. Table 2 indicates a type of each surface and a surface separation.
TABLE 1a: 4.0000E−03n: 1.51742OFFSET AMOUNT δE1E2E3E4TELEPHOTO END  3.00 mm−3.00 mm−1.18 mm  1.18 mmMIDDLE  0.29 mm−0.29 mm  2.18 mm−2.18 mmWIDE-ANGLE END−1.65 mm  1.65 mm  3.89 mm−3.89 mm
TABLE 2SURFACETYPE OF SURFACESEPARATIONOBJECTINFINITYSURFACES00REFERENCESURFACES1PLANE1S2POLYNOMIAL SURFACE0.5S3POLYNOMIAL SURFACE1S4PLANE0.4S50.4STOPSURFACES6PLANE1S7POLYNOMIAL SURFACE0.5S8POLYNOMIAL SURFACE1S9PLANE
A zoom lens is designed based on these values. FIG. 4 shows it. A ray incident upon a reference surface S0 enters a unit G1 first. The unit G1 includes two lenses E1 and E2, and surface numbers are labeled S1 to S4. The lenses E1 and E2 decenter in the Y-axis direction, and their decentering amounts continuously change. These amounts have the same absolute value and a positive and negative relationship. This configuration changes the power of G1 as shown in FIG. 2 from positive to negative. The light that exits from G1 passes a stop S5 and enters G2. Like G1, G2 includes two lenses E3 and E4, and surface numbers are labeled S6 to S9. The lenses E3 and E4 decenter in the Y-axis direction, and their decentering amounts continuously change. These amounts have the same absolute value and a positive and negative relationship. This configuration changes the power of G2 as shown in FIG. 2 from negative to positive.
The light that passes these lenses images without changing the image plane. However, it is understood from the image plane that large aberration occurs although an image is formed. The aberration occurs irrespective of the paraxial arrangements defined in Equation 10 and 11. For example, the paraxial arrangement cannot eliminate the coma that occurs on the optical axis. From the above result, the prior art cannot correct the aberration, because 1) an optical system having a rotationally asymmetrical lens is asymmetrical with respect to the optical axis, generates an offset between upper and lower rays, and consequently causes the coma for the on-axial light; and 2) the curvature of field occurs.